A lithographic apparatus is a machine that applies a desired pattern onto a substrate, usually onto a target portion of the substrate. A lithographic apparatus can be used, for example, in the manufacture of integrated circuits (ICs). In that instance, a patterning device, which is alternatively referred to as a mask or a reticle, may be used to generate a circuit pattern to be formed on an individual layer of the IC. This pattern can be transferred onto a target portion (e.g. comprising part of, one, or several dies) on a substrate (e.g. a silicon wafer). Transfer of the pattern is typically via imaging onto a layer of radiation-sensitive material (resist) provided on the substrate. In general, a single substrate will contain a network of adjacent target portions that are successively patterned. Known lithographic apparatus include so-called steppers, in which each target portion is irradiated by exposing an entire pattern onto the target portion at one time, and so-called scanners, in which each target portion is irradiated by scanning the pattern through a radiation beam in a given direction (the “scanning”-direction) while synchronously scanning the substrate parallel or anti-parallel to this direction. It is also possible to transfer the pattern from the patterning device to the substrate by imprinting the pattern onto the substrate.
In order to monitor the lithographic process, parameters of the patterned substrate are measured. Parameters may include, for example, the overlay error between successive layers formed in or on the patterned substrate and critical linewidth (CD) of developed photosensitive resist. This measurement may be performed on a product substrate and/or on a dedicated metrology target. There are various techniques for making measurements of the microscopic structures formed in lithographic processes, including the use of scanning electron microscopes and various specialized tools. A fast and non-invasive form of specialized inspection tool is a scatterometer in which a beam of radiation is directed onto a target on the surface of the substrate and properties of the scattered or reflected beam are measured. Two main types of scatterometer are known. Spectroscopic scatterometers direct a broadband radiation beam onto the substrate and measure the spectrum (intensity as a function of wavelength) of the radiation scattered into a particular narrow angular range. Angularly resolved scatterometers use a monochromatic radiation beam and measure the intensity of the scattered radiation as a function of angle.
By comparing the properties of the beam before and after it has been reflected or scattered by the substrate, the properties of the substrate can be determined. This can be done, for example, by comparing data obtained from measurement of the reflected or scattered beam with model (simulated) diffraction signals calculated from a parameterized model. The calculated signals can be pre-calculated and stored in a library, the library representing a plurality of candidate substrate structures distributed in a parameter space of the parameterized model. Alternatively or in addition, parameters can be varied during an iterative search process, until a calculated diffraction signal matches the measured signal. In U.S. Pat. No. 7,522,293 (Wu) and US 2012/0123748A1, for example, these two techniques are described for example as ‘library based’ and ‘regression based’ processes, respectively.
In particular for complex structures, or structures including particular materials, the number of parameters required to model the scattered beam accurately is high. A ‘model recipe’ is defined in which parameters are defined as either given (‘fixed’) or variable (‘floating’). For floating parameters, the permitted range of variation is defined, either in absolute terms or by reference to deviation from a nominal value. Each floating parameter in the model represents another ‘degree of freedom’ in the model, and consequently another dimension in the multidimensional parameter space in which the best matching candidate structure is to be found. Even with a handful of parameters, the size of computational tasks quickly becomes very large, for example by raising the number of library samples unacceptably. It also raises the risk of falsely matching parameter sets that do not correspond to the measured substrate. Fixing a parameter to a value that is not identical to what is actually in the measured structure in some cases may have little impact on the reconstruction. Other times, however, differences between the fixed value and the real value of the parameter may distort the matching process significantly so that inaccuracy arises in reconstruction of the parameters of interest. The fixed parameter in such a situation may be referred to as a “nuisance” parameter.
Such nuisance parameters make it difficult to find the right compromise between accuracy and practicality of computation. Nuisance parameters may be parameters of the model of the structure being measured, but they may also be parameters of an apparatus used to obtain measurements. That is to say, different apparatuses may obtain slightly different diffraction signals from the same structure, and therefore yield slightly different measurements of a parameter of interest.